Final Review Unit 1-4

Which of the following are examples of qualitative/categorical data?

• The airline on which a person chooses to book a flight

• The average number of women in chapters of the Gamma Goo sorority

• The closing Dow Jones average on 50 consecutive market days

• The scores on a given examination

• None of the above are examples of qualitative data

1. Free response questions on the AP Statistics Exam are graded on 4, 3, 2, 1, or 0 basis. Question #2 on the exam was of moderate difficulty. The average score on question #2 was 2.05 with a standard deviation of 1.To the nearest tenth, what score was achieved by a student who was at the 90th percentile of all students on the test? You may assume that the scores on the question were approximately Normally distributed.

• 3.5

• 3.3

• 2.9

• 3.7

• 3.1

Answer explanation

90th percentile -> 1.28 z-score

z = (x-2.05)/1

x=3.33

Tags

CCSS.HSS.ID.A.4

The first quartile (Q1) of a data set is 12 and the third quartile (Q3) is 18. What is the largest value above Q3 in the data set that would not be an outlier?

• 12

• 24

• 15

• 27

• 30

Answer explanation

IQR = 18 - 12 = 6

1.5 * IQR = 1.5 * 6 = 9

Outliers: [ Q1 - 1.5 * IQR, Q3 + 1.5 * IQR]

Bounds: [12-9,18+9 ] = [3,27]

In a Normal distribution with mean 25 and standard deviation 7, what proportion of values are less than 20?

• 0.71

• -0.71

• 0.24

• -0.24

• 0.76

Answer explanation

z = (20-25)/7 = -0.714

P(x<20) = P(z<-.0.714) = 0.2389

Tags

CCSS.HSS.ID.A.4

What are the mean, median, mode, and standard deviation of a Normal curve?u

• Mean = 1, median = 1, mode = 1, standard deviation = 1

• Mean = 1, median = 1, mode = 1, standard deviation = 0

• Mean = 0, median = 1, mode = 1, standard deviation = 1

• Mean = 0, median = 0, mode = 0, standard deviation = 1

• Mean = 0, median = 0, mode = 0, standard deviation = 0

Tags

CCSS.HSS.ID.A.4

6. Jenny is 5’10” tall and is wondering about her height. The heights of girls in the school are approximately Normally distributed with a mean of 5’5” and a standard deviation of 2.6”. What is the percentile rank of Jenny’s height?

• 59

• 65

• 74

• 92

• 97

Answer explanation

z = (70-65)/2.6 = 1.92

P(x<70) = P(z<1.92) =0.9726

Tags

CCSS.HSS.ID.A.4

The observation of 43 falls on a Normal distribution and its z-score is 1.65. If the mean of the distribution is 40, what is the standard deviation of the distribution?

• 3

• -1.82

• 0.55

• 1.82

• -0.55

Answer explanation

z = (x - mu)/(st. dev)

1.65 = (43-40)/ (st. dev)

st. dev = (43-40)/1.65= 1.82

Which of the following statements is (are) true?
I. The median is resistant to extreme values.
II. The mean is resistant to extreme values.
III. The standard deviation is resistant to extreme values.

• I only

• II only

• III only

• II and III only

• I and III only

The following histogram pictures the number of students who visited the Career Center each week during the school year. The shape of this graph could best be described as:

• Mound-shaped and symmetric

• Bi-modal

• Skewed to the left

• Uniform

• Skewed to the right

• 26.2

• 43.9

• -37.1

• -26.2

• 37.1

Answer explanation

score (hat) 273.5 + 91.2(3.0)= 547.1

residual = y - y-hat = 510 - 547.1 = -37.1

Tags

CCSS.HSS.ID.B.6B